Problem: Simplify the following expression: $p = \dfrac{21k}{-6k + 3}$ You can assume $k \neq 0$.
Find the greatest common factor of the numerator and denominator. The numerator can be factored: $21k = (3\cdot7 \cdot k)$ The denominator can be factored: $-6k + 3 = - (2\cdot3 \cdot k) + (3)$ The greatest common factor of all the terms is $3$ Factoring out $3$ gives us: $p = \dfrac{(3)(7k)}{(3)(-2k + 1)}$ Dividing both the numerator and denominator by $3$ gives: $p = \dfrac{7k}{-2k + 1}$